W just turned 4 months. The dr told us we could start solids if we wanted to but not to feel it was a necessity till closer to 6 months. They suggested an Iron fortified rice cereal, we have not decided what we are going to start with yet.
The cereal is a personal choice if it is working for you then ok, but starting it this early may have an effect on your supply. But I would also try spoon feeding it again. Just 1 spoon full mixed with BM till about a ketchup consistency is a good place to start. It will take her a few tries before she figures out how to actually get it to the back of her throat and swallow rather than just spitting it out. Solids are for learning and for fun before 1 year so don't stress to much about it, the main source of her nutrition for the 1st year should come from your milk.
To eliminate the night pumping I would pump right before bed. For me that is 10-1030ish. I am lucky and work where I can pump 3-4 times at work but still pump before bed to make sure that we have enough. W nurses much more often that your LO and adding a nursing session may also help your supply and pumping output. Here is what W day's are like.
His schedule is something like this.
630 wake and nurse till about 7 (some days he will wake as early as 545 those days we nurse twice in the morning)
730 get dropped at daycare
Most days he eats 3 4oz bottles (some days 2 and some days 4)
500 picked up
530 home and nurse
700 bedtime routine starts
He wakes 1-2 times a night and nurses.
Good Luck hope you find something that works for you both.